1. Field of the Invention
This invention relates to air circulation roller cone rock bits.
More particularly, this invention relates to moderate to high velocity and volume air circulation roller cone rock bits and a means formed in the rock bit to enhance rock chip removal from a borehole bottom as the bit works in the earth formation.
2. Description of the Prior Art
It is well known in the rock bit art to provide well fortified rock bit legs in multi-cone rock bits to assure that the rock bit maintains "gage" of a borehole while working in a formation. The leading edges of the shirttail portions of most of these bits are hardfaced to resist erosion of the bit shirttail since the shirttail portion is almost the same diameter as the cutting end of the rock bit. Additionally, the back of the leg is often studded with flush-type tungsten carbide inserts to resist erosion wear caused by the legs coming in contact with the borehole wall.
In petroleum drilling where the clearance around the rock bit is minimal, the liquid or drilling "mud" circulating fluid pumped into the drill string is sufficiently viscous to suspend the cuttings within itself and carry them out of the borehole at a relatively low rate of flow. With the introduction of air drilling, basic bit geometry did not change and the generally large detritus material in the borehole bottom .[.cound.]. .Iadd.could .Iaddend.not be carried out of the hole by the less dense and less viscous air until the rock particles were reduced in size by regrinding by the bit. Regrinding the detritus slowed down the formation penetration rate of the bit and shortened the life of the bit. The reground rock chips tend to dull the cutters and wear away the shirttail portion of the bit. In addition, the finely ground particles get into the bearing surfaces formed between the roller cones and the journals supported by the bit, further limiting bit life. It is imperative then that the borehole cuttings be immediately removed from the borehole bottom so that the bit cutting surface is continually exposed to uncut rock as it penetrates the formation.
The relative rock cuttings transport capabilities of liquid and gas drilling fluids are defined in the following analysis. Table 1 lists properties of rock cuttings transport capabilities of the fluids.
TABLE 1 ______________________________________ Properties of Rock Drilling Fluids ABSOLUTE PRESSURE DENSITY VISCOSITY TEMPER- pounds pounds pounds ATURE per square per cubic per foot- FLUID Fahrenheit inch feet second ______________________________________ Air 64 14.7 0.076 12.3 .times. 10.sup.-6 Air 165 54.7 0.236 14.1 .times. 10.sup.-6 Air 165 314.7 1.359 14.1 .times. 10.sup.-6 Water 68 -- 62.4 6.73 .times. 10.sup.-4 Mud 68 -- 75.0 336 .times. 10.sup.-4 Mud 68 -- 135.0 504 .times. 10.sup.-4 ______________________________________
A small spherical particle falling under the action of gravity through a viscous medium ultimately acquires a constant velocity expressed by Stokes' Law. ##EQU1## where
v=velocity (feet per second)
g=gravitational acceleration (feet per second per second)
a=radius of the sphere (feet)
d.sub.1 =density of the sphere (pounds per cubic foot)
.[.d.sub.1 .]. .Iadd.d.sub.2 .Iaddend.=density of the medium (pounds per cubic foot)
z=viscosity (pounds per foot second)
Using nominal particle size of one-eighth inch radius, particle density of 158 pounds per cubic foot.Iadd., .Iaddend.drilling mud density of 75 pounds per cubic foot, drilling mud viscosity of 0.0336 pounds per footsecond, and standard gravitational acceleration, we have: ##EQU2##
In theory, the velocity of the drilling mud up the annular area between the drilled hole wall and the outside diameter of the drill pipe must exceed this velocity to transport the assumed spherical rock cutting particle out of the drilled hole. In practice, most drilled rock cuttings tend to be flat or .[.lenz-shaped.]. .Iadd.lens-shaped .Iaddend.and Piggot.sup.1 suggests that the probable velocity will be about 40 percent of that calculated by the above equation. This gives good agreement with nominal drilling mud velocities encountered in practice and Allen.sup.2 where this velocity (called slip velocity) does not exceed 50 percent of the drilling mud annular velocity: EQU v(slip)=115 feet per minute.times.40%=46 feet per minute EQU Mud annular velocity=v(slip) 46 feet per minute.times.2=92 feet per minute
Stokes' law is applicable to viscous fluids only and cannot be applied to gaseous fluids. Even for high density air (314.7 pounds per square inch absolute pressure) the velocity becomes: ##EQU3## which is obviously absurd.
Where air is the cooling, lubricating, and flushing medium Gray.sup.3 developed the following equation for rock cutting particle velocity (slip velocity): ##EQU4## Where:
T=Bottom hole temperature (degrees Rankine)
P=Bottom hole pressure (pounds per square inch absolute)
Using the same rock particle data and air at 54.7 pounds per square inch absolute pressure, 160.degree. Fahrenheit (625.degree. Rankine) temperature, and assuming bottom hole pressure equal to delivered pressure: ##EQU5## For slip velocity at 50 percent of annular velocity we have: EQU Air Annular Velocity=V(slip)2130.times.2=4260 feet per minute
Annular fluid volume flow from: EQU Q=VA
Where:
Q=annular fluid volume flow (cubic feet per minute)
V=annular fluid velocity (feet per minute)
A=annular area (square feet)
For an 81/2 inch diameter rock bit with 5 inch outside diameter drill pipe, the annular area is 0.258 square feet and the annular fluid volume flow will be: EQU Q.sub.mud =92(0.258)=23.7 cubic feet per minute EQU Q.sub.air =4260(0.258)=1099 cubic feet per minute
These fluid velocities and volumes are typical for mud and air drilling conditions.
In this analysis, the mud and air drilling annular areas are equal for transporting the same size of particle. It should be noted, however, that the selected rock particle size is most closely related to the relatively low drilling penetration rates associated with mud drilling. It should also be noted that the selected rock particle density is most closely related to that of the shales, limestones, and sandstones associated with petroleum deposits where mud drilling is practiced. In mud drilling, the annular area and rock bit to hole wall clearance around the bit body are more than adequate. The flow of the incompressible mud is governed by bit nozzle diameters of less cross-sectional area than either the rock bit body clearance or the drilled hole annular area. Mud flow velocity through the nozzles, and therefore mud volume, is restricted by nozzle wear, cavitation effects, turbulence, pressure differentials, and available hydraulic horsepower.
Generally, air drilling produces large rock particle sizes and high drilling penetration rates, particularly for blast-hole drilling in surface mining where 50 foot maximum hole depths are typical. The compressible air flows contracting and expanding down the drill pipe, through rock bit nozzles and open air passages through the rock bit bearings, around the bit cutting structures and body, and up the drill pipe annular area. The annular area is usually adequate, but the rock bit to hole wall clearance around the bit body is often inadequate if designed to mud drilling standards. Additional bit body clearance is required for many air drilling applications to permit .[.passages.]. .Iadd.passage .Iaddend.of large rock particles and the greater volume of air required to transport the larger particles. Drilling penetration rates and related rock particle sizes commonly encountered in mud and air drilling are compared in Table 2.
TABLE 2 __________________________________________________________________________ Penetration Rates and Common Rock Particle Sizes MUD DRILLING CONDITIONS DRILLING AIR DRILLING __________________________________________________________________________ Slow Drilling Rate Penetration rates &lt;3 &lt;30 (feet per hour) Rock particle large &lt;1/4 &lt;1/4 dimensions (inches) Moderate Drilling Rate Penetration rates 3-20 30-100 (feet per hour) Rock particle large 1/4 1/4-1/2 dimensions (inches) High Drilling Rate Penetration rates &gt;20 &gt;100 (feet per hour) Rock particle large &gt;1/4 &gt;1/2 dimensions (inches) __________________________________________________________________________
The volume of rock cuttings passed over the bit body and up the drilled hole annular area is not significant for mud or air drilling. Table 3 shows the volume of rock particles removed from an 81/2 inch diameter hole (0.394 square feet cross-sectional area) at various penetration rates.
TABLE 3 ______________________________________ Volume of Rock Particles Removed Penetration Rate Penetration Rate Volume of Rock Removed (feet per hour) (feet per minute) (cubic feet per minute) ______________________________________ 3 0.05 0.019 10 0.17 0.065 30 0.50 0.197 60 1.00 0.394 100 1.67 0.652 ______________________________________
For a penetration rate of 160 feet per hour and using slip velocities equal to 50 percent of the fluid velocities previously calculated (92 feet per minute for mud drilling and 4260 feet per minute for air drilling), the areas required to transport the rock cuttings will be: ##EQU6## which is less than 10 percent of the annular area (0.258 square feet) ##EQU7## which is less than 0.2 percent of the annular area.
Using Gray's equation, the larger rock particle sizes for moderate (3/8 inch rock particle large dimensions) to high (1/2 inch rock particle large dimensions) air drilling rates will produce a corresponding increase of one and one-half to two times the air velocity (6390 to 8520 feet per minute) and resulting air volume (1649 to 2198 cubic feet per minute) flowing in the drilled hole annular area.
Although the relatively high penetration rate air drilling practices of surface mining are possible in petroleum drilling, the constraints of directional control, maintaining hole diameter for emplacing casing, and avoiding bit damage to preclude premature removal of a lengthy drill string from a deep hole dictate deliberately slow drilling. In contrast, surface mining blast hole air drilling permits rough directional control, rough hole diameter control, since casing is not emplaced, and is virtually insensitive to bit damage and bits are drilled to destruction. Consequently, higher penetration rates and larger chips, with a corresponding requirement for greater clearance between the mining bit body and the drilled hole wall, are normal for virtually all surface mining air drilling relative to petroleum drilling.
As a practical matter, the clearance between a bit body and the drilled hole wall cannot be greater than the clearance between the shoulder of the threaded connection at the threaded pin end of the bit. This clearance is further restricted by the requirement for bit shirttail structural integrity, including allowances for lubricating and cooling passages. Using the bit cross-sectional clearance area through the threaded jet nozzles relative to the drilled hole annular area we have the following typical ratios:
Petroleum bit ratio=0.28
Mining bit ratio=0.37
Mining air drilling bit clearance areas should be at least 37 percent of the available area and should be about 30 percent more than that of a comparable petroleum mud drilling bit.
Experience has shown that in state of the art mining bits, the penetration rate is slow, wear rate is rapid and a heightened erosion rate of the shirttail leg portion of each of the bits is evident. Therefore, the present invention overcomes these major problems in the mining industry. This is accomplished through careful removal of material from the shirttail portion of the rock bit, thus providing greater clearance so the rock chips or detritus may more easily pass from the borehole bottom up the drill string and out of the formation.